So far although experimental evidences of black hole thermodynamics have not been found, people still expect that black hole thermodynamics should have some observational signatures, for example the quasinormal modes (QNMs), which may be detected from astronomical observations in the future. Recently, the authors in Refs. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]} had found that QNMs indeed exhibit characteristic behaviours along the black hole phase transition. Thus QNMs can be use to probe the phase transition of black holes in AdS/dS spacetime. Especially there is a dramatic change of the slope of QNMs along with the black hole phase transition [6]}. These results indicate that there is a close connection between the dynamical and thermodynamical aspects of black holes. In addition, as we well known that QNMs are intimately linked to the unstable photon orbits [13]}, [14]}, [15]}, then they are playing an important role in strong gravitational phenomena (such as the shadow, lensing, and gravitational waves) [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}. In short, QNMs can be regarded as the vibration frequencies of photon orbits and can be derived by the photon orbits [25]}. Based on these observations, it is natural to construct the relation between the photon orbits and black hole phase transitions and to check out whether properties of photon orbits can signal the black hole phase transition.
